 SPHERE_LEBEDEV_RULE
Quadrature Rules for the Sphere

SPHERE_LEBEDEV_RULE is a dataset directory which contains files
defining Lebedev rules on the unit sphere, which can be used for
quadrature, and have a known precision.

A Lebedev rule of precision p can be used to correctly integrate any
polynomial for which the highest degree term xiyjzk satisfies i+j+k <=
p.

The approximation to the integral of f(x) has the form Integral
f(x,y,z) = 4 * pi * sum ( 1 <= i < n ) wi * f(xi,yi,zi) where

        xi = cos ( thetai ) * sin ( phii )
        yi = sin ( thetai ) * sin ( phii )
        zi =                  cos ( phii )
      

The data file for an n point rule includes n lines, where the i-th
line lists the values of

        thetai phii wi
      

The angles are measured in degrees, and chosen so that:

        - 180 <= thetai <= + 180
            0 <= phii <= + 180
      

and the weights wi should sum to 1.

Licensing:

The computer code and data files described and made available on this
web page are distributed under the GNU LGPL license.

Downloaded from:

http://people.sc.fsu.edu/~jburkardt/datasets/sphere_lebedev_rule/sphere_lebedev_rule.html
